How to prove sole custody of dependent

Am putting application in for a visa for settlement for my husband-to-be and his 5 year old daughter. The mother left the child with him once finished breastfeeding and he has brought her up by himself (with own familys help) since then. The mother sees child about once a year.

1. Can anyone advise me? How does my husband prove sole custody? We are not sure what to provide in way of evidence except for birth certificate and letter from mother agreeing to child leaving the country. Anyone got any ideas? No point getting legal paper as this proves nothing as sole custody could have been granted anytime. (eg just in order to send child overseas)

I gather this is a very tricky one and lots of dependents get rejected. Particularly hard if father is the carer/sole parent as this is rarer I guess. Wondering whether it is the strength of my husbands case which will decide the fate of the little one, or if we can do anything else to strengthen her claim. I fear that if she is refused my husband will not come over to settle here and we will have to carry on this long distance relationship and keep appealing! Dont want to waste the money on visas too if neither are likely to come here!!

2. Lastly, when filling in aplication form for her VAF4A in section 8.5, am I the sponsor or is it her father who is applying at the same time?

Court order is usually required.